Finite temperature corrections to a NLO Nambu-Jona-Lasinio model
Marco Frasca
备注：
4 pages, 2 figures. Contribution to the proceedings of the 19th International Conference in Quantum Chromodynamics (QCD 16), 4 July - 8 July 2016, Montpellier (France).Added the reference to the review by Brodsky, de Teramond and Deur
发表信息：
Nuclear and Particle Physics Proceedings 282-284, 173-176 (2017)
We derive the next-to-leading order correction to the Nambu-Jona-Lasinio model starting from quantum chromodynamics. So, we are able to fix the constants of the Nambu-Jona-Lasinio model from quantum chromodynamics and analyze the behavior of strong interactions at low energies. The technique is to expand in powers of currents the generating functional. We apply it to a simple Yukawa model with self-interaction showing how this has a Nambu-Jona-Lasinio model and its higher order corrections as a low-energy limit. The same is shown to happen for quantum chromodynamics in the chiral limit with two quarks. We prove that a consistent thermodynamic behaviour is obtained as expected for the given parameters.
We investigate the QCD phase diagram at zero chemical potential and finite temperature in the presence of an external magnetic field within the three flavor Polyakov-Nambu-Jona-Lasinio and entangled Polyakov-Nambu-Jona-Lasinio models looking for the inverse magnetic catalysis. Two scenarios for a scalar coupling parameter dependent on the magnetic field intensity are considered. These dependencies of the coupling allow to reproduce qualitatively lattice QCD results for the quark condensates and for the Polyakov loop: due to the magnetic field the quark condensates are enhanced at low and high …
It is shown that the difference between the magnetic moment results in the quark model with null instantons and semibosonized Nambu-Jona-Lasinio model lies in the description of the magnetic moment of the $ Λ$-hyperon.
The QCD phase diagram at zero chemical potential and finite temperature subject to an external magnetic field is studied within the three flavor Nambu--Jona-Lasinio (NJL) model and the NJL model with the Polyakov loop (PNJL). A scalar coupling parameter dependent on the magnetic field intensity is considered. The scalar coupling has been fitted so that the lattice QCD pseudocritical chiral transition temperatures are reproduced and in the limit of large magnetic field decreases with the inverse of the magnetic field intensity. This dependence of the coupling allows to reproduce the lattice QCD…
In a previous work, we proposed an extended Nambu--Jona-Lasinio (NJL) model including heavy quark flavors. In this work, we will calculate strong and radiative decays of vector mesons in this extended NJL model, including light $ρ$, $ω$, $K^*$, $ϕ$ and heavy $D^*$, $D^*_s$, $B^*$, $B^*_s$.
In present report we review some preliminary results of investigation of higher orders of mean-field expansion for Nambu--Jona-Lasinio model. We discuss first results of investigation of next-to-next-to-leading order of mean-field expansion equations for four-quark and three-quark Green functions. We have considered equations for Green functions of Nambu--Jona-Lasinio model in mean-field expansion up to third order.
The polarization effects of the processes $τ\rightarrow K^{-} π^{0} ν_τ$ are described in the framework of the Nambu--Jona-Lasinio model. The intermediate vector meson $K^{*}(892)$ is taken into account. The contribution of these effects to the differential decay width is obtained.
Nambu-Jona-Lasinio model used to investigate low energy phenomena is nonrenormalizable, therefore the results depend on the regularization parameter in general. A possibility of the finite in four-dimensional limit and even the regularization parameter (this is dimension in the dimensional regularization scheme) independent analysis is shown in the leading order of the 1/Nc expansion.
We review the effect on vacuum properties and magnetic catalysis, of adding the most general 0-spin 8-quark (8q) interactions to the combined SU(3) flavor Nambu--Jona-Lasinio (NJL) and 6-quark (6q) 't Hooft interaction Lagrangian.
The electromagnetic dipole and quadrupole polarizabilities of the neutral and charged pions are calculated in the Nambu--Jona-Lasinio model. Our results agree with the recent experimental analysis of these quantities based on Dispersion Sum Rules. Comparison is made with the results from the Chiral Perturbation Theory.
The survival of \bar q q bound states at temperatures higher than the chiral restoration temperature, T_c, recently observed in lattice QCD, is discussed in the framework of the Nambu Jona-Lasinio model. The perturbative determination of the spectral function provides an indication of a pseudogap phase above T_c.
The full and differential widths of the decay $τ\rightarrow K^{0}K^{-}ν_τ$ are calculated in the framework of the extended Nambu-Jona-Lasinio model. The contributions of the subprocesses with the intermediate vector mesons $ρ$(770) and $ρ$(1450) are taken into account. The obtained results are in satisfactory agreement with the experimental data.
The vacuum structure for a Nambu-Jona -Lasinio type model is studied using the effective potential approach. The relevant degrees of freedom are taken to be two different sets of static, auxiliary fields with different symmetry properties, related by Fierz transformations in the action. The results are compared with the analysis of the Dyson-Schwinger equations in the one-loop approximation.
It is shown that in the one-flavour NJL model the vector and axial-vector quasiparticles described by the antisymmetric tensor field are generated. These excitations have tensor interactions with quarks in contrast to usual vector ones. Phenomenological applications are discussed.
We investigate the phase diagram on temperature-chemical potential plane in the Nambu-Jona-Lasinio model with the dimensional regularization. While the structure of the resulting diagram shows resemblance to the one in the frequently used cutoff regularization, some results of our study indicate striking difference between these regularizations. The diagram in the dimensional regularization exhibits strong tendency of the first order phase transition.
The decay width of the process eta -> pi^0 gamma gamma is calculated in the framework of the Nambu-Jona-Lasinio model. The momentum dependence of quark loops is taken into account. Three types of diagrams are considered: quark box, scalar(a0) and vector(rho, omega) pole diagrams. The obtained estimations are in satisfactory agreement with recent experimental data.
Using the description of the subprocess $γγ^*\to S(P)$ in terms of local Nambu-Jona-Lasinio model we calculate the cross sections of photoproduction of scalar and pseudoscalar mesons in high energy photon-lepton collisions processes. The dependence on the transversal momentum and the total cross sections in Weizsaecker-Williams approximation are presented.
We investigate the compositeness condition in four dimensions at the non-trivial order (next-to-leading order in $1/N$ with the number $N$ of the colors), taking the Nambu-Jona-Lasinio model as an example. In spite of its non-renormalizability, the compositeness condition can be successfully derived and solved in compact forms. The resultant problems are discussed.
The behavior of the quark condensates at zero chemical potential and finite temperature subject to an external magnetic field is studied within the three flavor Nambu--Jona-Lasinio model with Polyakov loop (PNJL) and its extension, the so-called entangled PNJL model (EPNJL). A comparison with recent lattice QCD data is performed and it is shown that at $T=0$ MeV the light quark condensates are in quantitative agreement. At finite temperature, although there is an overall reasonable agreement with several lattice results, it is shown that in the lattice calculations the effect due to the electr…
The Nambu-Jona-Lasinio model is the special case of the renormalized Yukawa model with the compositeness condition. We use it to calculate the effective coupling constants in terms of the compositeness sale (momentum cut off) at the next-to-leading order in 1/N. The next-to-leading correction is too large in the model of scalar composite, while that in the induced gauge theory is reasonably suppressed due to the gauge cancellation of the leading divergences.
The nonet meson properties are studied in the Nambu-Jona-Lasinio model at finite temperature and chemical potential using dimensional regularization. This study leads to the reasonable description which is mainly similar to one obtained in the model with the cutoff regularization. However, remarkable differences between the two regularizations are observed in the behavior of the chiral phase transition at finite chemical potential.
The effective dimensional reduction of fermion-antifermion pairing dinamics in Nambu-Jona-Lasinio model in external chromomagnetic field is considered. It is shown that such a field causes the reduction of the space dimension by one unit in contrast to an ordinary magnetic field which reduces it by two units. The enhancement of the dynamical chiral symmetry breaking due to the reduction is discussed.
In the Nambu - Jona-Lasinio model the decay widths $τ\to (π, π'(1300)) ν_τ$ were calculated. For the calculation of the decay width $τ\to πν_τ$ the standard NJL model was used with taking into account the intermediate axial-vector meson and the extended Nambu - Jona-Lasinio model with the intermediate $a_1(1260)$ and $a_1'(1647)$ mesons. These results are in good agreement with each other. For the calculation of the decay width $τ\to π' ν_τ$ extended Nambu - Jona-Lasinio model was used. The results are in satisfactory agreement with the experimental data. Numerical estimates for the constant $…
We argue that the extended Nambu-Jona-Lasinio model which introduces four-quark interactions to describe hadron physics at low energies can be confronted with fundamental quantum chromodynamics by means of spectral sum rules. While there arise rather restrictive bounds on the strength of the effective four-quark interaction in the vector channel, introduction of the four-quark interaction in the pseudoscalar channel resolves a long standing puzzle of the sum rules.
It is shown that in the Nambu -- Jona - Lasinio model at nonzero chemical potential there are two different massive phases with spontaneously broken chiral symmetry. In one of them particle density is identically zero, in another phase it is not equal to zero. The transition between phases is a phase transition of the second order.
We propose an extended Nambu--Jona-Lasinio model to include the heavy mesons with the heavy quark symmetry. The quark current-current interaction is generalized to include the heavy quark currents. In order to comply with the heavy quark spin symmetry at the heavy quark limit, the quark mass dependence of the interaction strength is introduced. The light and heavy pseudo-scalar and vector meson, their masses and the weak decay constants, are calculated in the unified frame.
We present the results for the pion electromagnetic quadrupole polarizabilities, calculated within the Nambu--Jona-Lasinio model. We obtain the sign and magnitude in agreement with the respective experimental analysis based on the Dispersion Sum Rules. At the same time the dipole polarizabilities are well reproduced. Comparison is also made with the results from the Chiral Perturbation Theory.
The polarizability of a charged pion is estimated in the framework of the nonlocal chiral quark model of the Nambu--Jona-Lasinio type. Nonlocality is described by quark form factors of the Gaussian type. It is shown that the polarizability in this model is very sensitive to the form of nonlocality and choice of the model parameters.
Scalar meson contributions in chiral quark condensate are calculated for analytically regularized Nambu -- Jona-Lasinio model in framework of mean-field expansion in bilocal-source formalism. Sigma-meson contribution for physical values of parameters is found to be small. Pion contribution is found to be significant and should be taken into account at the choice of the parameter values.
We analyze the analytic structure of meson propagators in the Nambu--Jona-Lasinio model with a proper-time regulator. We show that the regulator produces unphysical complex singularities. As a result the naive use of the Wick rotation is no longer allowed. Formulas involving integration over mesonic momenta, such as meson-loop contributions or dispersion relations for meson Green's functions, cannot be written in usual forms.
The Nambu--Jona-Lasinio model is investigated in the $1/N_c$ expansion with the dimensional regularization. At the four-dimensional limit the meson propagators have simple forms in the leading order of the $1/N_c$ expansion. Thus the next to leading order calculation reduces to an ordinary one loop calculation. Here we obtain an explicit form of the $1/N_c$ correction and numerically evaluate the $N_c$ dependence for the gap equation.
The electric polarizability of the nucleon is calculated in the soliton approach to the Nambu--Jona-Lasinio model. We analyze the leading-$N_c$ contributions, as well as the effects of rotational $1/N_c$ corrections and $Δ$-$N$ mass splitting. Our model prediction is substantially reduced compared to other soliton calculations, and is closer to the experimental value.
The Nambu - Bogoliubov - de Gennes method is applied to the problem of superconducting QCD. The effective quark-quark interaction is described within the framework of the Nambu - Jona-Lasinio model. The details of the phase diagram are given as a function of the strength of the quark-quark coupling constant $G^{\prime}$. It is find that there is no superconducting phase transition when one uses the relation between the coupling constants $G^{\prime}$ and $G$ of the Nambu - Jona-Lasinio model which follows from the Fierz transformation. However, for other values of $G^{\prime}$ one can find a r…
We discuss the quark masses and the elastic $q\bar q$ cross sections at finite chemical potential in the Nambu--Jona-Lasinio model. We comment the generic features of the cross sections as functions of the chemical potential, temperature and collision energy. Finally, we discuss their relevance in the construction of a relativistic transport model for heavy-ion collisions based on this effective Lagrangian.
The electromagnetic properties of the SU(3) octet baryons are investigated in the semibosonized SU(3) Nambu--Jona-Lasinio model.The rotational $1/N_c$ and strange quark mass corrections in linear order are taken into account. It turns out that the model is in good agreement with the experimental data.
We investigate the chiral phase transition at finite temperature and chemical potential within SU(2) and SU(3) Nambu-Jona-Lasinio type models. The behavior of the baryon number susceptibility and the specific heat, in the vicinity of the critical end point, is studied. The class of the critical points is analyzed by calculating critical exponents.
We study the phase diagram of the three flavor Polyakov-Nambu-Jona Lasinio (PNJL) model and in particular the interplay between chiral symmetry restoration and deconfinement crossover. We compute chiral condensates, quark densities and the Polyakov loop at several values of temperature and chemical potential. Moreover we investigate on the role of the Polyakov loop dynamics in the transition from nuclear matter to quark matter.
A short introduction to quark models with four fermion terms and their predictions for the parameters of low-energy effective Lagrangians is given. Special attention is paid to predictions that are as general as possible. Contribution to the Second DAPHNE Physics Handbook, eds. L. Maiani, G. Pancheri and N. Paver.
Two-parton correlations in the pion, a non perturbative information encoded in double parton distribution functions, are investigated in the Nambu and Jona-Lasinio model. It is found that double parton distribution functions expose novel dynamical information on the structure of the pion, not accessible through one-body parton distributions, as it happens in several estimates for the proton target and in a previous evaluation for the pion, in a light-cone framework. Expressions and predictions are given for double parton distributions corresponding to leading-twist Dirac operators in the quark…
We present a calculation of the coupling constants in the massive spin-1 field chiral Lagrangian to chiral ${\cal O}(p^3)$ in the context of an extended Nambu--Jona-Lasinio cut-off model. Phenomenological applications of this Lagrangian to anomalous and non-anomalous low-energy hadronic transitions involving spin-1 particles are also discussed.
We discuss the phenomenology of SU(3) Skyrme and Nambu--Jona-Lasinio models. We show that while the Skyrme model, in its simplest version, is unable do reproduce the hyperon spectrum, the NJL model describes both hyperon and isospin splittings with satisfactory accuracy. The difference between the two models lies in new {\em anomalous} moments of inertia, which vanish in the Skyrme model and get non-zero contribution from the {\em valence} quarks in the NJL model
We study the regularization dependence on meson properties and the phase diagram of quark matter by using the two flavor Nambu-Jona-Lasinio model. We find that the meson properties and the phase structure do not show drastically difference depending the regularization procedures. We also find that the location or the existence of the critical end point highly depends on the regularization methods and the model parameters. Then we think that regularization and parameters are carefully considered when one investigates the QCD critical end point in the effective model studies.
We derive the effective action for pseudoscalar mesons by integrating out vector and axial--vector collective fields in the generating functional of the bosonized NJL--model. The corresponding modifications of the nonlinear effective Lagrangian and the bosonized currents, arising at $O(p^4)$, are discussed.
The nonlocal Polyakov-loop-extended Nambu--Jona-Lasinio (PNJL) model is further improved by including momentum-dependent wave-function renormalization in the quark quasiparticle propagator. Both two- and three-flavor versions of this improved PNJL model are discussed, the latter with inclusion of the (nonlocal) 't Hooft-Kobayashi-Maskawa determinant interaction in order to account for the axial U(1) anomaly. Thermodynamics and phases are investigated and compared with recent lattice-QCD results.
The dynamical breakdown of the $SU(2) \times U(1)$ symmetry triggered by a top-antitop condensate is studied in a supersymmetric version of the gauged Nambu-Jona-Lasinio model. An effective potential approach is used to investigate the vacuum structure and the equivalence with the minimal supersymmetric standard model. The role of the soft supersymmetry breaking terms is analyzed in detail in a version of the model where the electroweak gauge interactions are turned off.
We calculate the thermal evolution of $π-π$ scattering lengths, in the frame of the Nambu--Jona-Lasinio model. The thermal corrections were calculated at the one loop level using Thermofield Dynamics. We present also results for the pion thermal mass. Our procedure implies the modeling of a propagating scalar meson as a resumation of chains of quark bubbles, which is presented explicitly. We compare our results with previous analysis of this problem in the frame of different theoretical approaches.
We estimate the slope of the topological susceptibility in the three flavour Nambu-Jona-Lasinio model with the 't Hooft interaction. The results are consistent with the evaluation from the QCD sum rule in favour of the full topological susceptibility. We apply it to the Shore-Veneziano formula to find that it shows satisfactory agreement with the anomalous suppression of the flavour-singlet axial charge. The behaviour at finite temperature is also discussed.
We argue that the extended Nambu-Jona-Lasinio model of hadrons can be be probed and constrained in a nontrivial way via QCD sum rules. While there arise rather restrictive bounds on the strength of the effective four-fermion interaction in the vector channel, introduction of the four-fermion interaction in the pseudoscalar channel could resolve a long standing puzzle of QCD sum rules. We speculate also on possible connection between effective four-quark interactions describing the low-energy phenomenology and ultraviolet renormalons of the fundamental QCD.
In the extended Nambu - Jona - Lasinio model the decay widths $τ\rightarrow ρ(770) (ρ'(1450)) ν_τ$ and $τ\rightarrow K^{*}(892) (K^{*'}(1410)) ν_τ$ are studied in the quark one -loop approximation. Our estimations of the decay widths $τ\rightarrow K^{*}(892) (K^{*'}(1410)) ν_τ$ are in satisfactory agreement with experimantal data. In the paper, the decay widths $τ\rightarrow ρ(770) (ρ'(1450)) ν_τ$ are also calculated.
The effect of Polyakov loop on the QCD phase diagram at high density is studied within the Nambu-Jona Lasinio model with Polyakov loop (PNJL model). We point out that the color neutrality is missing in the standard PNJL model at finite density. Moreover, we discuss how the color-flavor locked (CFL) phase is to be distorted by the inclusion of Polyakov loop.
Gaugino condensation in the hidden sector of supergravity models is described within a Nambu-Jona-Lasinio type of approach by minimization of a one-loop scalar potential. The essential ingredients of the mechanism are auxiliary superfields whose v.e.v. generate gaugino condensation and supersymmetry breaking, introduced through Lagrange multipliers. For phenomenologically acceptable values of the gauge couplings, gaugino condensation is disfavoured in this approach. For completeness, it is shown that supersymmetry breaking would occur for a stronger coupling, but at a scale inconsistent with t…
We evaluate the next-to-leading order correction to the Nambu-Jona-Lasinio model starting from quantum chromodynamics. We show that a systematic expansion exists, starting from a given set of exact classical solutions, so that higher order corrections could in principle be computed at any order. In this way, we are able to fix the constants of the Nambu-Jona-Lasinio model from quantum chromodynamics and analyze the behavior of strong interactions at low energies. The technique is to expand in powers of currents of the generating functional. We apply it to a simple Yukawa model with self-intera…
We treat quantum chromodynamics (QCD) using a set of Dyson-Schwinger equations derived, in differential form, with the Bender-Milton-Savage technique. In this way, we are able to derive the low energy limit that assumes the form of a non-local Nambu-Jona-Lasinio model with all the parameters properly fixed by the QCD Lagrangian and the determination of the mass gap of the gluon sector.
In this paper, chiral symmetry breaking and its restoration are investigated in the mean field approximation of Nambu--Jona-Lasinio model. A first-order phase transition exists at low temperature, but is smeared out at high temperature. We discuss the rationality of using susceptibilities as the criteria to determine the crossover region as well as the critical point. Based on our results, it is found that to define a critical band instead of an exclusive line in this region might be a more suitable choice.
We show the existence of a pseudogap phase in the Nambu Jona-Lasinio model of quark interactions. In the pseudogap phase chiral symmetry is restored but q\bar q pseudoscalar mesons still exist and they are massive. Such a behavior is intermediate between a BCS superconductor and a Bose Einstein Condensate. We suggest the relevance of this phenomenon for an understanding of recent lattice QCD and experimental data.
A non-local Nambu-Jona-Lasinio model can be derived from QCD in the low-energy limit. In this way, it is possible to fix all the free parameters of the model with physical ones. We used this approach to derive a local limit to the Nambu-Jona-Lasinio model, with the parameters those obtained from QCD, in order to fix the physical parameters of $ρ$ condensation and obtain the critical magnetic field. $ρ$ condensation is a consequence of the highly non-trivial behavior of the QCD vacuum in presence of a very strong magnetic field giving rising to superconductive behavior in quark matter. We exten…
Thermodynamic properties of strongly interacting matter are investigated using the Polyakov loop enhanced Nambu$-$Jona-Lasinio model along with some modifications to include the hadrons. Various observables are shown to have a close agreement with the numerical data of QCD on lattice. The advantage of the present scheme over a similar study using a switching function is that here no extra parameters are to be fitted. As a result the present scheme can be easily extended for finite chemical potentials.
We apply the closed time-path Green function formalism in the Nambu--Jona-Lasinio model. First of all, we use this formalism to obtain the well-known gap equation for the quark condensate in a stationary homogeneous system. We have also used this formalism to obtain the Ginzburg-Landau (GL) equation and the time-dependent Ginzburg-Landau (TDGL) equation for the chiral order parameter in an inhomogeneous system. In our derived GL and TDGL equations, there is no other parameters except for those in the original NJL model.
In this article we study the nonlocal Nambu--Jona-Lasinio model with a Gaussian regulator in the chiral limit. Finite temperature effects and the presence of a homogeneous magnetic field are considered. The magnetic evolution of the critical temperature for chiral symmetry restoration is then obtained. Here we restrict ourselves to the case of low magnetic field values, being this a complementary discussion to the exisiting analysis in nonlocal models in the strong magnetic field regime.
A regularization for the baryon number consistent with the energy in the Nambu-Jona-Lasinio model is introduced. The soliton solution is constructed with the regularized baryon number constrained to unity. It is furthermore demonstrated that this constraint prevents the soliton from collapsing when scalar fields are allowed to be space dependent. In this scheme the scalar fields actually vanish at the origin reflecting a partial restoration of chiral symmetry. Also the influence of this constraint on some static properties of baryons is discussed.
